The main result is a fixed point theorem for compositions of chain faithful mttltifunctions (Corollary 2.3). The theorem is then applied to get sufficient conditions for the fixed point property of the product of two partially ordered sets. For the Special Issue on the NIH Conference on Universal Algebra & Lattice Theory

‎the purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎the results presented in the paper generalize and extend several well-known results in the literature‎.

We look for geometric structures which underlie both the 'classical' geometric and more modern 'order theoretic' conditions for a Banach space (dual space) to have the weak (weak*) fixed point property; that is, for every nonexpansive self-mapping of a nonempty weak (weak*) compact convex subset to have a fixed point.

The main result of this paper is that every non-reflexive subspace Y of L 1 [0, 1] fails the fixed point property for closed, bounded, convex subsets C of Y and nonexpansive (or contractive) mappings on C. Combined with a theorem of Maurey we get that for subspaces Y of L 1 [0, 1], Y is reflexive if and only if Y has the fixed point property. For general Banach spaces the question as to whether...